AP EAMCET · Maths · Indefinite Integration
\(\int \frac{2 x^2-3}{\left(x^2-4\right)\left(x^2+1\right)} d x=\mathrm{Atan}^{-1} x+\mathrm{B} \log (x-2)+\mathrm{C} \log (x+2)\)
then \(6 A+7 B-5 C=\)
- A \(9\)
- B \(10\)
- C \(6\)
- D \(8\)
Answer & Solution
Correct Answer
(A) \(9\)
Step-by-step Solution
Detailed explanation
\(\int \frac{\left(2 x^2-3\right)}{\left(x^2-4\right)\left(x^2+1\right)} d x=\int \frac{\left(2\left(x^2+1\right)-5\right)}{\left(x^2-4\right)\left(x^2+1\right)} d x\) \(=\int \frac{2}{x^2-4} d x-\int\left(\frac{1}{x^2-4}-\frac{1}{x^2+1}\right) d x\)…
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